Abstract

Given a continuous distribution of acoustic sources, the determination of the source strength that ensures the synthesis of a desired sound field is shown to be identical to the solution of an equivalent acoustic scattering problem. The paper begins with the presentation of the general theory that underpins sound field reproduction with secondary sources continuously arranged on the boundary of the reproduction region. The process of reproduction by a continuous source distribution is modeled by means of an integral operator (the single layer potential). It is then shown how the solution of the sound reproduction problem corresponds to that of an equivalent scattering problem. Analytical solutions are computed for two specific instances of this problem, involving, respectively, the use of a secondary source distribution in spherical and planar geometries. The results are shown to be the same as those obtained with analyses based on High Order Ambisonics and Wave Field Synthesis, respectively, thus bringing to light a fundamental analogy between these two methods of sound reproduction. Finally, it is shown how the physical optics (Kirchhoff) approximation enables the derivation of a high-frequency simplification for the problem under consideration, this in turn being related to the secondary source selection criterion reported in the literature on Wave Field Synthesis.

Received 21 December 2012Revised 31 August 2013Accepted 23 September 2013

Acknowledgments:

This work has been partially funded by the Royal Academy of Engineering and by the Engineering and Physical Sciences Research Council, UK.

Article outline:I. INTRODUCTIONII. FORMULATION OF THE SOUND FIELD REPRODUCTION PROBLEMIII. THE SINGLE LAYER POTENTIAL AND THE JUMP RELATIONIV. EQUIVALENT SCATTERING PROBLEMV. SPHERICAL GEOMETRY AND ANALOGY WITH HIGH ORDER AMBISONICSVI. PLANAR AND LINEAR GEOMETRY AND WAVE FIELD SYNTHESISVII. OTHER GEOMETRIES AND HIGH FREQUENCY SCATTERINGVIII. CONCLUSIONS